As a development economist you are interested in whether ind

As a development economist, you are interested in whether individuals in country A have a lower mean income than those in country B. You have available independent simple random samples of size 50 each from the two populations. In these samples, X vector_A = $500 S_A = 200 X vector_B = $600 S_B = 300 Assuming that the population variances are equal, find the prob-value for and test the hypothesis H_0 : Mu - Mu_A = 0 H_1 : Mu _B - Mu_A> 0 at the .05 level.

Solution

Test Statistic
X (Mean)=500; Standard Deviation (s.d1)=200
Number(n1)=50
Y(Mean)=600; Standard Deviation(s.d2)=300
Number(n2)=50
Value Pooled variance S^2= (n1-1*s1^2 + n2-1*s2^2 )/(n1+n2-2)
S^2 = (49*40000 + 49*90000) / (100- 2 )
S^2 = 65000
we use Test Statistic (t) = (X-Y)/Sqrt(S^2(1/n1+1/n2))
to=500-600/Sqrt((65000( 1 /50+ 1/50 ))
to=-100/50.9902
to=-1.9612